
Using i.i.d. condition of \(\lbrace X_t\rbrace _{t\ge 1}\)  and negatively associativity of \(\lbrace Z_t\rbrace _{t\ge 1}\) , it follows that for \(s>0\) , \(\mathbb {E}[\exp (sY)]\le \prod \limits _{l=t-\tau +1}^t \mathbb {E}[\exp (sY_l)]\) . Moreover, \(Y_l\in [ -ac_{\text{max}}, 1-ac_{\text{min}}]\) . Then the result follows by Hoeffding's inequality [1]}, [2]}.
